Beurling–Lax theorem

In mathematics, the Beurling–Lax theorem is a theorem due to Beurling (1949) and Lax (1959) which characterizes the shift-invariant subspaces of the Hardy space $H^2(\mathbb{D},\mathbb{C})$. It states that each such space is of the form

$\theta H^2(\mathbb{D},\mathbb{C}),$

for some inner function $\theta$.

See also

• H²

References

• Jonathan R. Partington, Linear Operators and Linear Systems, An Analytical Approach to Control Theory, (2004) London Mathematical Society Student Texts 60, Cambridge University Press.
• Marvin Rosenblum and James Rovnyak, Hardy Classes and Operator Theory, (1985) Oxford University Press.